On domination number of Latin square graphs of finite cyclic groups

This paper aims to find certain bounds for the domination number of Latin square graphs, i.e., a simple graph assigned to a Latin square. In fact, we show that if [Formula: see text] is a Latin square of order [Formula: see text] and [Formula: see text] is the associated Latin square graph of [Formula: see text], then [Formula: see text]. We will investigate in which case the equalities hold. Finally, we study the domination number of Latin square graph associated to groups. In particular, we show that if [Formula: see text], then [Formula: see text]. Also, we prove that if [Formula: see text], then [Formula: see text].

Solvable groups whose character degree graphs generalize squares

Let G be a solvable group, and let {\Delta(G)} be the character degree graph of G. In this paper, we generalize the definition of a square graph to graphs that are block squares. We show that if G is a solvable group so that {\Delta(G)} is a block square, then G has at most two normal nonabelian Sylow subgroups. Furthermore, we show that when G is a solvable group that has two normal nonabelian Sylow subgroups and {\Delta(G)} is block square, then G is a direct product of subgroups having disconnected character degree graphs.

Non-exterior square graph of finite group

We define the non-exterior square graph ??G which is a graph associated to a non-cyclic finite group with the vertex set G\?Z(G), where ?Z(G) denotes the exterior centre of G, and two vertices x and y are joined whenever x ^ y ? 1, where ^ denotes the operator of non-abelian exterior square. In this paper, we investigate how the group structure can be affected by the planarity, completeness and regularity of this graph.

On Square Divisor Cordial Graphs

The square divisor cordial labeling is a variant of cordial labeling and divisor cordial labeling. Here we prove that the graphs like flower Fln, bistar Bn,n, square graph of Bn,n, shadow graph of Bn,n as well as splitting graphs of star Kl,n and bistar Bn,n are square divisor cordial graphs. Moreover we show that the degree splitting graphs of Bn,n and Pn admit square divisor cordial labeling. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved.doi: http://dx.doi.org/10.3329/jsr.v6i3.16412 J. Sci. Res. 6 (3), 445-455 (2014)

Vertex Equitable Labeling of Cyclic Snakes and Bistar Graphs

Let G be a graph with p vertices and q edges and let A = {0, 1, 2,..., }. A vertex labeling f: V (G) ® A induces an edge labeling f * defined by f *(uv) = f(u) + f(v) for all edges uv. For , let vf (a) be the number of vertices v with f(v) = a. A graph G is said to be vertex equitable if there exists a vertex labeling f such that for all a and b in A, and the induced edge labels are 1, 2, 3, , q. In this paper, we establish vertex equitable labeling of square graph of and splitting graph of and kC4 –snake(k?1) and the generalized kCn –snake is vertex equitable if nº0(mod4),n?4. Keywords: Vertex equitable labeling; Vertex equitable graph. © 2014 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. doi: http://dx.doi.org/10.3329/jsr.v6i1.15044 J. Sci. Res. 6 (1), 79-85 (2014)